#matrix-calculus

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5 questions · 5 min · score and explanations at the end

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For a nonzero vector $\mathbf{v} \in \mathbb{R}^n$ , what is the gradient $\frac{\partial}{\partial\mathbf{v}}\lVert\mathbf{v}\rVert_2$ ?

$\mathbf{v}/\lVert\mathbf{v}\rVert_2$ , the unit vector along $\mathbf{v}$ 1
$2\mathbf{v}$ , twice the vector itself2
$\mathbf{v}/\lVert\mathbf{v}\rVert_2^2$ , the vector divided by its squared norm3
$\mathbf{1}$ , a vector of ones, as each $v_i$ enters the norm once4

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